This worked for me, but I guess it would depend upon your cable.
I have a Macbook Pro 13" Mid 2010 with mini display port.
I had my Samsung 46" LCD TV permanently connected to a HDMI cable and that cable permanently connected to the Moshi Mini Display Port to HDMI Adapter.
Before Mavericks, I used to just then put the mini display port into my Mac and as long as I selected the right source on my TV (HDMI4), up it came.
After the upgrade to Mavericks, when I plug the cable in I got the normal flash, while the resolutions sort themselves out, but then no input on the TV screen.
I once had success by putting it to sleep, by using the apple menu, waited for the little light on the front to start flashing to indicate it was asleep, then waking it with the cable in, but didn't work the next day.
I may have been me playing with the display modes (CMD-F1) ,but haven't got that method working again since.
And tonight I stumbled up a way to get it working.
Instead of removing the adapter from the macbook, remove the HDMI cable from the adapter and plug it in again. Works every time now. If you have an all in one cable, try removing it from the TV end and plugging it in again.
How bizaare.